Solve for u. 42 = –7(u + 41)

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The equation your teacher has given you is an identity. We can prove this by transforming one side into the other. I'll transform the right hand side (RHS) into the left hand side (LHS).

This means I'll keep the LHS the same for each line. I'll only change the RHS. The goal is to get the same thing on both sides (I could go the other way around but I find this pathway is easier).

[tex]\tan^4(\theta)+\sec^2(\theta) = \sec^4(\theta)-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\sec^2(\theta)\right)^2-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\tan^2(\theta)+1\right)^2-\tan^2(\theta) \ \text{ ... see note 1}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+2\tan^2(\theta)+1-\tan^2(\theta)\\\\[/tex]

[tex]\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\tan^2(\theta)+1\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta)-1+1 \ \text{ ... see note 2}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta) \ \ \Large \checkmark\\\\[/tex]

So because we've arrived at the same thing on both sides, the original equation is an identity. It always true no matter what theta value you plug in, as long as theta is in the domain. So something like theta = pi/2 won't work because tan(pi/2) = undefined and sec(pi/2) = undefined. It's based on how cos(pi/2) = 0 and this value is in the denominator. Dividing by zero is undefined.

Consequently, this means all solutions to cos(theta) = 0 will be excluded from the domain. Everything else works.

Answer:

2/5m - 1/5

Step-by-step explanation:

Given the equation :

2(1/5m - 2/5) + 3/5

First step:

Open the bracket by multiplying values in the bracket by 2

2/5m - 4/5 + 3/5

-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5

Hence,

2/5m - 4/5 + 3/5 = 2/5m - 1/5

= 2/5m - 1/5

Answer:

G: 4x + 0.25 = 4.5x

Step-by-step explanation:

1. since Jazzie runs 4 mph add .5 to that to get Jocelyn's speed of 4.5 mph

2. Since Jazzie has a head start add .25 to 4x to get 4x + 0.25 = ?

3. put Jocelyn's speed in the question Mark to get 4x + 0.25 = 4.5x

Answer:

-41

Step-by-step explanation:

f(x) = 4x + 3 and g(x) = -2x + 5

g(f(5) ) =

First find f(5) = 4(5)+3 = 20+3 = 23

Then find g(23) = -2(23) +5 = -46+5 = -41

Answer:

rational

Step-by-step explanation:

it can be written as a fraction

Answer:

Observational study

Step-by-step explanation:

A type of study which does not involve giving the participants or subjects any sort of treatment or undergoing any test. The participants are simply observed or studied over a cwetina period of time on the basis of what the researcher intends to measure before coming up with a conclusion. In the scenario above, employees eating habits is studied without having to undergo any sort of treatment or test, they are only studied in terms of what they eat and other measures of interest.

Answer:

The radius of the circle if the circumference is 44 cm will be 7 cm.

Step-by-step explanation:

➝ Circumference of the circle = 44 cm

➔ Circumference = 2πr [For finding radius]

Finding the radius:-

➜ Let radius be r.

➜ 44 = 2 × 22/7 × r

➜ Multiply 2 × 22/7

➜ 44 = 44/7 × r

➜ Taking 7 to LHS.

➜ 44 × 7 = 44 × r

➜ 308 = 44 × r

➜ Taking 44 to LHS.

➜ 308/44 = r

➜ 308/44 = 7

➜ 7 = r

➜ r = 7

Answer:

84°

Step-by-step explanation:

angles in a quadrilateral add to 360°. 360-(114+76)=5x =170°. 170°/5 = 32°. x=32°

angles on a straight line add to 180°.

2x = 64°. 180-64=116°. y=116°.

y-x = 116-32 = 84°

Answer:

[tex]78[/tex]

Step-by-step explanation:

The inner angles of a quadrilateral all add up to 360. This means we can write the following

[tex]114 + 76 + 3x + 2x = 360\\190 + 5x = 360\\5x = 170\\x = 34[/tex]

Now that we have x we can find y. Notice that y and 2x are on the same line. Any line cutting another straight line will create two angles that add up to 180.

Therefore we can write

[tex]2x + y = 180\\2(34) + y = 180\\y = 112[/tex]

Finally computing y - x

[tex]y - x = 112 - 34 = 78[/tex]

Explanation:

The square has perimeter P = 16, so each side of the square is P/4 = 16/4 = 4 cm.

This makes side KJ = 4 cm, and this is the diameter of the circle. Multiply the diameter with pi to get the circumference (aka the perimeter of the circle).

Therefore, the perimeter is pi*d = pi*4 = 4pi which points us to choice B

Answer:

g(x)=x+9

Step-by-step explanation:

When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x

therefore, g(x)=x+9

Answer:

g(x)=x-8

Step-by-step explanation:

-2+2 = 0, so g(x) = x

5-13 = -8

Answer:

Step-by-step explanation:

Choice A is the only one that is applicable.

Answer:

A. F(x) has 1 relative minimum and maximum.

Step-by-step explanation:

[tex]{ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}[/tex]

As x and F(x) tend to positive and negative infinity:

[tex]{ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}[/tex]

❎So, B and C are excluded.

Roots of the polynomial:

[tex]{ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}[/tex]

❎, D is also excluded.

✔, A

Answer:

19 units

Step-by-step explanation:

count the squares around the shape for the slanted part treat it like a rectangle and just count the squares from the pointy spot to the other side where it stops

In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.

If the 15th term is 40, then

40 = -12 + (15 - 1) c   ==>   c = 52/14 = 26/7

We can then write the n-th term as

-12 + (n - 1) 26/7 = (26n - 110)/7

The sum of the first 15 terms is then

[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]

Another way to compute the sum: let S denote the sum,

S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40

Reverse the order of terms:

S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12

Notice that adding up terms in the same position gives the same result,

-12 + 40 = 28

-58/7 + 254/7 = 28

-32/7 + 228/7 = 28

so that

S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28

There are 15 terms in the sum, so

2S = 15×28   ==>   S = 15×28/2 = 210

Answer:

12.73

Step-by-step explanation:

Set up ratio.

[tex]\frac{22}{100} =\frac{2.89}{x}[/tex]

Solve for x.

[tex]\frac{100}{22} =\frac{x}{2.8}[/tex]

[tex]\frac{100}{22} (2.8)=x[/tex]

x=12.73

Answer:

y=x

Step-by-step explanation:

so,

((x - -2)² + (y - 4)²) - ((x - 3)² + (y - -1)²) = 10

(x² + 4x + 4 + y² - 8y + 16) - (x² - 6x + 9 + y² + 2y + 1) = 10

x² + 4x + y² - 8y + 20 - x² + 6x - y² - 2y - 10 = 10

10x - 10y = 0

y = x

Answer:

228573

Step-by-step explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an)         [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d     [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

    = 129(2237)

    = 228573

Answer:

28.9°

Step-by-step explanation:

The golfer, hole and spectator form a triangle. Let ABC be the triangle and let the angle the spectator has between the golfer and the hole be A = 110°, the angle the golfer has between the spectator and the hole be B and the angle the hole has between the golfer and the spectator be C. Let the angle between the golfer and the hole be a = 200 yards, the distance between the spectator and the hole be b and the distance between the golfer and the spectator be c = 140 yards,

Using the sine rule for the triangle, we find angle C.

So, a/sinA = b/SinB = c/SinC

So, a/sinA = c/sinC

sinC = csinA/a

C = sin⁻¹(csinA/a)

Substituting the values of the variables into the equation, we have

C = sin⁻¹(csinA/a)

C = sin⁻¹( 140sin110°/200)

C = sin⁻¹( 7 × 0.9397/10)

C = sin⁻¹(6.5778/10)

C = sin⁻¹(0.65778)

C = 41.13°

We know that A + B + C = 180°  (sum of angles in a triangle)

And since the angle the golfer has between the spectator and the hole be B

So, B = 180° - (A + C)

B = 180° - (110° + 41.13°)

B = 180° - 151.13°

B = 28.87°

B ≅ 28.9°

The angle that the golfer has between the spectator and the hole is 28.9°.

Using the law of sines:

BC/SinΔBAC=AB/SinΔACB

Hence,

200/Sin110°=140/SinΔACB

ΔACB=41.1°

Thus,

ΔABC=180°-ΔBAC-ΔACB

ΔABC= 180° - (110° + 41.1°)

ΔABC= 180° - 151.1°

ΔABC= 28.9°

Inconclusion the angle that the golfer has between the spectator and the hole is 28.9°.

Learn more angle here:https://brainly.com/question/25770607

Answer:

The x-coordinate is –4

The y-coordinate is –1

The point is in the quadrant Third quarter ( 3 )

I hope I helped you^_^

Answer:

4(g + p).

Step-by-step explanation:

The sum of g and p is g + p.

Next we multiply this sum by 4.

We need to place the g + p in parentheses to do this.

Answer:

-1/3 · Ix+4I + 5

or

y∠ - Ix+4I -15

            3

Step-by-step explanation:

hope this helped

Answer:

5ba^2 +ab^2 6a^2 + 2b

Step-by-step explanation:

ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)

6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b

6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b

5ba^2 +ab^2 6a^2 + 2b

Answer:

The bigger angle is 144 degrees and the smaller one is 36 degrees

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

Answer:

£3780

Step-by-step explanation:

P= £3500, R=4%, t=2years

I = PRT/100

I= (3500×4×2)/100 =£280

Amount in 2years = P+I = £3500+ £280= £3780

Answer:

P1 =(-6,-2)

P1=8

P2(-4,-1)

P2=5

Answer:

x = 21.4

Step-by-step explanation:

We need to use the law of sins

sin 42       sin x

--------- = ----------

22              12

12 sin 42 = 22 sin x

12 sin 42 /22 = sin x

Taking the inverse sin of each side

sin^-1(12/22 sin 42) = sin^-1(sin x)

21.40637223 =x

To the nearest tenth

x = 21.4